What is the Greatest Common Factor of 30045 and 30060?

Greatest common factor (GCF) of 30045 and 30060 is 15.

GCF(30045,30060) = 15

We will now calculate the prime factors of 30045 and 30060, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30045 and 30060.

How to find the GCF of 30045 and 30060?

We will first find the prime factorization of 30045 and 30060. After we will calculate the factors of 30045 and 30060 and find the biggest common factor number .

Step-1: Prime Factorization of 30045

Prime factors of 30045 are 3, 5, 2003. Prime factorization of 30045 in exponential form is:

30045 = 3¹ × 5¹ × 2003¹

Step-2: Prime Factorization of 30060

Prime factors of 30060 are 2, 3, 5, 167. Prime factorization of 30060 in exponential form is:

30060 = 2² × 3² × 5¹ × 167¹

Step-3: Factors of 30045

List of positive integer factors of 30045 that divides 30045 without a remainder.

1, 3, 5, 15, 2003, 6009, 10015

Step-4: Factors of 30060

List of positive integer factors of 30060 that divides 30045 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 167, 180, 334, 501, 668, 835, 1002, 1503, 1670, 2004, 2505, 3006, 3340, 5010, 6012, 7515, 10020, 15030

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30045 and 30060. The biggest common factor number is the GCF number.
So the greatest common factor 30045 and 30060 is 15.

Also check out the Least Common Multiple of 30045 and 30060